Výsledky vyhledávání - "Hofstadler, Julian"

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Optimal convergence rates of MCMC integration for functions with unbounded second moment

Autor: Hofstadler, Julian

We study the Markov chain Monte Carlo (MCMC) estimator for numerical integration for functions that do not need to be square integrable w.r.t. the invariant distribution. For chains with a spectral gap we show that the absolute mean error for $L^p$ f

Externí odkaz: http://arxiv.org/abs/2403.16920

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Almost sure convergence rates of adaptive increasingly rare Markov chain Monte Carlo

Autor: Hofstadler, Julian, Latuszynski, Krzysztof, Roberts, Gareth O., Rudolf, Daniel

We consider adaptive increasingly rare Markov chain Monte Carlo (AIR MCMC), which is an adaptive MCMC method, where the adaptation concerning the past happens less and less frequently over time. Under a contraction assumption for a Wasserstein-like f

Externí odkaz: http://arxiv.org/abs/2402.12122

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Consistency of randomized integration methods

Autor: Hofstadler, Julian, Rudolf, Daniel

We prove that a class of randomized integration methods, including averages based on $(t,d)$-sequences, Latin hypercube sampling, Frolov points as well as Cranley-Patterson rotations, consistently estimates expectations of integrable functions. Consi

Externí odkaz: http://arxiv.org/abs/2203.17010

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The Spherical Cap Discrepancy of HEALPix Points

Autor: Ferizović, Damir, Hofstadler, Julian, Mastrianni, Michelle

In this paper we show that the spherical cap discrepancy of the point set given by centers of pixels in the HEALPix tessellation (short for Hierarchical, Equal Area and iso-Latitude Pixelation) of unit $2$-sphere is lower and upper bounded by order s

Externí odkaz: http://arxiv.org/abs/2203.07552

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